A boat moves upstream with speed u relative to water in a river. A package falls from the boat unnoticed. After time T the boatman notices it, instantly turns around, and moves downstream with the same speed u relative to water. The time after turning required to catch the package is:
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Question

A boat moves upstream with speed u relative to water in a river. A package falls from the boat unnoticed. After time T the boatman notices it, instantly turns around, and moves downstream with the same speed u relative to water. The time after turning required to catch the package is:

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G1 Physics · Accepted Answer

In the water frame the package is stationary. The boat moves away from it with speed u for time T, so separation becomes uT. After turning, the boat approaches with speed u relative to the water frame. Thus catch-up time = uT/u = T.